Randomized phase III trial to compare the effectiveness of combination chemotherapy, surgery, and radiation therapy with or without dexrazoxane and trastuzumab in treating women who have stage IIIA, stage IIIB or stage IV breast cancer. Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Chemoprotective drugs, such as dexrazoxane, may protect normal cells from the side effects of chemotherapy. Monoclonal antibodies such as trastuzumab can locate tumor cells and either kill them or deliver tumor-killing substances to them without harming normal cells. Radiation therapy uses high-energy x-rays to damage tumor cells. It is not yet known if chemotherapy combined with surgery and radiation therapy is more effective with or without dexrazoxane and trastuzumab in treating breast cancer